The difference between low and high tide where I live is about 4 metres. I know it is less in some places and a lot more in others.
Logic seems to tell me that if something the size of the moon influences something the size of the ocean by a mere 4 metres, and the amount of water in a tree by comparison is who-knows-how-much less than the ocean, it makes sense that the effect would be nil or non existent.
I somewhat agree that a full moon has an effect on animals, but is there evidence that this is because of the water content in their bodies? Seems like a massive increase in light during nighttime would probably have more of an effect than some kind of gravitational pull on H2O molecules... and even if its true, you'd have to prove how that affects behaviour in animals, on a biological level.
Reading SLIMBOB's post kind of makes me think the moon DOES affect trees and animals, but maybe it's the light? It is afterall SUN light, the same as what a plant gets during the day.
If you had extra sunlight during the night with which to lay down wood, at whatever rate, wouldn't that explain it?